Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

被引：2516
|
作者：
Branicky, MS [1 ]
机构：
[1] Case Western Reserve Univ, Dept Elect Engn & Appl Phys, Cleveland, OH 44106 USA
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 1998年 / 43卷 / 04期
关键词：
hybrid systems; limit cycles; Lyapunov methods; nonlinear systems; stability; switched systems; variable-structure systems;
D O I：
10.1109/9.664150
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we introduce some analysis tools for switched and hybrid systems, We first present work on stability analysis, We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems (IFS) theory as a tool for Lagrange stability, We also discuss the case where the switched systems are indexed by an arbitrary compact set, Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
引用
收藏
页码：475 / 482
页数：8
相关论文
共 50 条
  • [1] DISCOVERING MULTIPLE LYAPUNOV FUNCTIONS FOR SWITCHED HYBRID SYSTEMS
    She, Zhikun
    Xue, Bai
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (05) : 3312 - 3340
  • [2] A NOTE ON MULTIPLE LYAPUNOV FUNCTIONS AND STABILITY CONDITION FOR SWITCHED AND HYBRID SYSTEMS
    Zhai, Guisheng
    Matsune, Isatada
    Imae, Joe
    Kobayashi, Tomoaki
    [J]. INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL, 2009, 5 (05): : 1189 - 1199
  • [3] A note on multiple Lyapunov functions and stability condition for switched and hybrid systems
    Zhai, Guisheng
    Matsune, Isatada
    Imae, Joe
    Kobayashi, Tomoaki
    [J]. PROCEEDINGS OF THE 2007 IEEE CONFERENCE ON CONTROL APPLICATIONS, VOLS 1-3, 2007, : 254 - 259
  • [4] Discovering Multiple Lyapunov Functions for Switched Hybrid Systems with Global Exponential Stability
    Lu, Junjie
    She, Zhikun
    Xue, Bai
    [J]. 2015 54TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2015, : 4252 - 4259
  • [5] Common and Multiple Lyapunov Functions in Stability Analysis of Nonlinear Switched Systems
    Vassilyev, S. N.
    Kosov, A. A.
    [J]. 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES (ICNPAA 2012), 2012, 1493 : 1066 - 1073
  • [6] A Multiple Lyapunov Functions Approach for Stability of Switched Systems
    Lu, Jin
    Brown, Lyndon J.
    [J]. 2010 AMERICAN CONTROL CONFERENCE, 2010, : 3253 - 3256
  • [7] Harmonic Lyapunov functions in the analysis of periodically switched systems
    Almer, S.
    Jonsson, U. T.
    [J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 2759 - 2764
  • [8] Stability analysis for discrete-time switched systems based on multiple Lyapunov functions
    Li Huimin
    Bai Xiaoming
    Yang Xiaosong
    [J]. PROCEEDINGS OF THE 26TH CHINESE CONTROL CONFERENCE, VOL 2, 2007, : 59 - 61
  • [9] Computing multiple Lyapunov-like functions for inner estimates of domains of attraction of switched hybrid systems
    Zheng, Xiuliang
    She, Zhikun
    Lu, Junjie
    Li, Meilun
    [J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2018, 28 (17) : 5191 - 5212
  • [10] Analysis of Hybrid Systems' Dynamics Using the Common Lyapunov Functions and Multiple Homomorphisms
    Vassilyev, S. N.
    Kosov, A. A.
    [J]. AUTOMATION AND REMOTE CONTROL, 2011, 72 (06) : 1163 - 1183
12345